My mom states how sick she is every few minutes, but is mentally sharp. How do I deal with this in a normal way?

As you know elderly people will complain about their health continually to anyone within earshot and complain incessantly about how sick they are all day long.
If your mother is repeating the same thing or asking the same question over and over again, that's a dementia loop. People with dementia get fixated on something and repeat about it over and over again and often for days at a time.
Have your mother checked out by her doctor. Her dizziness could be any number of things. Then you have to break the dementia loop.
Answer her a few times and then stop answering. When she repeats again tell her a few times that you've already answered her and will not be discussing it further. Then ignore her when she's repeating whatever she's fixated on in the loop. Don't ignore her in other ways though. If she asks you something not related to the loop she's in, answer her. Offer her a snack or a cup of coffee, or whatever she likes. Put the tv on for her. Any distraction. Ingore what the dementia loop is about. She will get out of it.

You state in your profile that mom has Alzheimer's.
So given that diagnosis she is NOT mentally sharp.
She may be in some aspects but not all.
It all depends on what part of the brain is effected as to what she can and can not do.
Repeating questions is common.
As long as she is physically ok, and you have had the dizzy spells checked by her doctor, reassure her that she is fine.
redirect her. Tell her that maybe a bit of tea, coffee, juice and a bit of toast or fruit might make her feel better.
Make sure that if she is having dizzy spells that she is safe to walk by herself. Use a walker if she needs to. (with or without wheels, ask a PT or OT what would be best)
With the dementia and if she is aware that her memory is failing then she is correct in that she is "sick" and this might be frightening for her. She just needs to know that you will be there, that you will help her if she needs it. Hold her hand and tell her that you love her.

Repeating is a common dementia/memory loss issue. You don't have to respond to the comment because you know she'll keep doing it plus she won't remember that you didn't respond. I find it exhausting, so I either give a minimal 1-syllable response (like "huh"), ignore it completely, respond with a completely different topic, walk out of the room or put on the tv or other diversion for my LO.

I've learned a lot from Teepa Snow videos on YouTube where you can learn about dementia and better ways to interact with LOs who have challenging behaviors. Her mental sharpness may be what's in her long-term memory, which is how memory loss is, the short-term goes first.

Your profile says your mom has dementia.

Many folks with dementia repeat statements or questions all day long.

Go to Alz.org to read up on this.

Try asking your mom specific qiestions about how she feels, rather than open-ended ones.

If a person keeps repeating the same statement over and over, it may be sign of poor memory. She could be "sharp" in other aspects, but her bad memory prevents her to remember that she already told you the same thing before. What to do? just listen and give her the same answer.

i find it really hard to take such questions seriously.

honestly --- OP are you being serious??

are you a troll? this is a fake question?

if your mother's dizzy, i'm sure you've seen a doctor about it? if you haven't, you're deeply neglecting your mother.

if your mother keeps repeating things -- surely, you've seen a doctor about that too? maybe she really is physically sick, and needs help? maybe she's mentally not ok (dementia), if she keeps repeating things?

you must have seen a doctor about this.
it's totally bizarre to post such a question to random people who are not doctors, and who don't know your mother's health.